Preheat the oven to 350°F (175°C). Line two baking sheets with parchment paper.
In a large bowl, cream together the peanut butter, softened unsalted butter, granulated sugar, and light brown sugar until smooth and fluffy.
Beat in the egg and vanilla extract until well combined.
In a separate bowl, whisk together the all-purpose flour, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Stir in the rolled oats and semisweet chocolate chips until evenly distributed.
Drop rounded tablespoons of dough onto the prepared baking sheets, spacing them about 2 inches apart.
Bake in the preheated oven for 10 to 12 minutes, or until the edges are lightly golden but the centers remain soft.
Remove from the oven and allow the cookies to cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely.